Question

The ac series circuit is composed of a resistance of 20 \(\Omega\), inductive reactance of 40 \(\Omega\) and capacitive reactance of 15 \(\Omega\). If a current of 1 Ampere is flowing, then what is the applied voltage value?

• A. 320V
• B. 22V
• C. 32V
• D. 220V

Hint:

Series RLC Circuit. Impedance \( Z = \sqrt{R^2 + (X_L - X_C)^2 \). Applied Voltage \( V = I \times Z \). Ensure all values (V, I) are consistent (e.g., both RMS or both peak).

Answer 1

The Correct Option is C

In a series RLC circuit, the total impedance (Z) determines the relationship between applied voltage (V) and current (I) according to Ohm's Law: V = I * Z
Given: Resistance \(R = 20 \, \Omega\) Inductive Reactance \(X_L = 40 \, \Omega\) Capacitive Reactance \(X_C = 15 \, \Omega\) Current \(I = 1 \, \text{A}\) (assuming RMS value) The total impedance Z is calculated as: $$ Z = \sqrt{R^2 + (X_L - X_C)^2} $$ $$ Z = \sqrt{(20)^2 + (40 - 15)^2} $$ $$ Z = \sqrt{400 + (25)^2} $$ $$ Z = \sqrt{400 + 625} $$ $$ Z = \sqrt{1025} \, \Omega $$ Calculate the square root: \(\sqrt{1025} \approx 3(2)0156\) \(\Omega\)
Let's round it to 32 \(\Omega\) for simplicity, as the options are integers
\(Z \approx 32 \, \Omega\)
Now, calculate the applied voltage V: $$ V = I \times Z $$ $$ V \approx (1 \, \text{A}) \times (32 \, \Omega) = 32 \, \text{V} $$ The applied voltage value is approximately 32 V